100 results found for "number and square" in Class 10.
The square of a positive number is (60) more than (11) times the number. What is the number?
B. (15)
समीकरण \(x^2=11x+60\) है। \(x^2-11x-60=0\) से धनात्मक हल (x=15) है। / The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).
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The square of a number is (2800) more than (30) times the number. What is the positive number?
C. (70)
समीकरण \(x^2=30x+2800\) है। \(x^2-30x-2800=0\) से धनात्मक हल (70) है। / The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).
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The square of a number is (640) more than (24) times the number. What is the positive number?
C. (40)
समीकरण \(x^2=24x+640\) है। \(x^2-24x-640=0\) से धनात्मक हल (40) है। / The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).
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The square of a number is (432) more than (18) times the number. What is the positive number?
C. (36)
समीकरण \(x^2=18x+432\) है। \(x^2-18x-432=0\) से धनात्मक हल (36) है। / The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).
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The square of a number is (54) more than (15) times the number. What is the positive number?
A. (18)
यदि संख्या (x) है, तो \(x^2=15x+54\)। \(x^2-15x-54=0\) से धनात्मक संख्या (18) है। / If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
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The square of a number is (42) more than (11) times the number. What is the positive number?
A. (14)
यदि संख्या (x) है, तो \(x^2=11x+42\)। \(x^2-11x-42=0\) से धनात्मक हल (14) है। / If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
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The square of a number is (240) more than (14) times the number. What is the positive number?
B. (24)
समीकरण \(x^2=14x+240\) है। \(x^2-14x-240=0\) से धनात्मक हल (24) है। / The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).
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The square of a number is (24) more than (10) times the number. What is the positive number?
A. (12)
यदि संख्या (x) है, तो \(x^2=10x+24\)। \(x^2-10x-24=0\) से धनात्मक संख्या (12) है। / If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).
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The sum of the square of a positive number and (5) times the number is (84). What is the number?
B. (7)
समीकरण \(x^2+5x=84\) है। इससे (x=7) या (x=-12) मिलता है और उत्तर (7) है। / The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).
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The square of a positive number is (28) more than (3) times the number. What is the number?
C. (7)
समीकरण \(x^2=3x+28\) है। इससे (x=7) या (x=-4) मिलता है और धनात्मक उत्तर (7) है। / The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).
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The square of a positive number is (22) more than (9) times the number. What is the number?
B. (11)
संख्या (x) हो, तो \(x^2=9x+22\), यानी \(x^2-9x-22=0\)। धनात्मक मूल (11) है। / Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).
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The square of a positive number is (384) more than (8) times the number. What is the number?
C. (24)
\(x^2=8x+384\) से \(x^2-8x-384=0\), जिससे (x=24) मिलता है। वाक्य को सही क्रम में समीकरण बनाइए। / \(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.
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The square of a positive number is (187) more than (6) times the number. What is the number?
C. (17)
\(x^2=6x+187\) से \(x^2-6x-187=0\), जिसका धनात्मक हल (17) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें। / \(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.
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The square of a number is (60) more than (11) times the number. What is the positive number?
B. (15)
\(x^2=11x+60\) से \(x^2-11x-60=0\), जिसका धनात्मक हल (15) है। अधिक का अर्थ समीकरण में जोड़ना होता है। / \(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.
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The square of a positive number is (120) more than (2) times the number. What is the number?
C. (12)
\(x^2=2x+120\) से \(x^2-2x-120=0\) और (x=12) मिलता है। वाक्य को सही क्रम में समीकरण में बदलें। / \(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.
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The square of a positive number is (70) more than (3) times the number. What is the number?
B. (10)
\(x^2=3x+70\) से \(x^2-3x-70=0\) बनता है और धनात्मक हल (10) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल न लें। / \(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.
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The square of a number is (18) more than (7) times the number. What is the positive number?
B. (9)
\(x^2=7x+18\) से \(x^2-7x-18=0\) और धनात्मक हल (9) है। वाक्य में अधिक का अर्थ जोड़ना होता है। / \(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.
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The square of a positive number is (45) more than (4) times the number. What is the number?
C. (9)
\(x^2=4x+45\) से \(x^2-4x-45=0\) मिलता है और धनात्मक हल (9) है। ऐसे प्रश्न में वाक्य को सीधे समीकरण में बदलें। / \(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.
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The square of a positive number is (24) more than (5) times the number. What is the number?
C. (8)
समीकरण \(x^2=5x+24\) है, यानी \(x^2-5x-24=0\), जिससे धनात्मक हल (x=8) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें। / The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.
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Which number is equal to \(\sqrt{9.61}\) on the number line?
A. (3.1)
क्योंकि \(3.1^2=9.61\), इसलिए \(\sqrt{9.61}=3.1\)। दशमलव वर्गों को सावधानी से गुणा करें। / Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.
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Which number is equal to \(\sqrt{9}\) on the number line?
A. (3)
\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है। / \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
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The sum of a number and its square is (2352). What is the positive number?
C. (48)
\(x^2+x=2352\) से \(x^2+x-2352=0\) मिलता है। धनात्मक हल (48) है। / \(x^2+x=2352\) gives \(x^2+x-2352=0\). The positive solution is (48).
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The sum of a number and its square is (1892). What is the positive number?
C. (43)
\(x^2+x=1892\) से \(x^2+x-1892=0\) मिलता है। धनात्मक हल (43) है। / \(x^2+x=1892\) gives \(x^2+x-1892=0\). The positive solution is (43).
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The sum of a number and its square is (1260). What is the positive number?
C. (35)
\(x^2+x=1260\) से \(x^2+x-1260=0\) मिलता है। धनात्मक हल (35) है। / \(x^2+x=1260\) gives \(x^2+x-1260=0\). The positive solution is (35).
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The sum of a number and its square is (930). What is the positive number?
C. (30)
\(x^2+x=930\) से \(x^2+x-930=0\) मिलता है। धनात्मक हल (30) है। / \(x^2+x=930\) gives \(x^2+x-930=0\). The positive solution is (30).
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The sum of a number and its square is (72). What is the positive number?
A. (8)
मान लें संख्या (x) है, तो \(x^2+x=72\)। \(x^2+x-72=0\) से धनात्मक हल (8) है। / Let the number be (x), so \(x^2+x=72\). From \(x^2+x-72=0\), the positive solution is (8).
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The sum of a number and its square is (342). What is the positive number?
B. (18)
\(x^2+x=342\) से \(x^2+x-342=0\), इसलिए (x=18) है। योग वाले प्रश्न में दोनों पद सीधे जोड़ें। / \(x^2+x=342\) gives \(x^2+x-342=0\), so (x=18). In sum questions, add both terms directly.
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The sum of a number and its square is (156). What is the positive number?
C. (12)
\(x^2+x=156\) से \(x^2+x-156=0\), इसलिए (x=12) है। संख्या और उसके वर्ग के योग को सीधे लिखें। / \(x^2+x=156\) gives \(x^2+x-156=0\), so (x=12). Write the sum of the number and its square directly.
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The sum of a number and its square is (42). What is the positive number?
B. (6)
\(x^2+x=42\) से \(x^2+x-42=0\), इसलिए (x=6) है। संख्या और वर्ग के योग को सीधे समीकरण में बदलें। / \(x^2+x=42\) gives \(x^2+x-42=0\), so (x=6). Convert the sum of number and square directly into an equation.
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The sum of a positive number and its square is (156). What is the number?
C. (12)
संख्या (x) हो, तो \(x^2+x=156\)। इससे \(x^2+x-156=0\), इसलिए धनात्मक मूल (12) है। / Let the number be (x), then \(x^2+x=156\). This gives \(x^2+x-156=0\), so the positive root is (12).
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When (9) times a number is added to its square, the result is (400). What is the positive number?
A. (16)
समीकरण \(x^2+9x=400\) है। \(x^2+9x-400=0\) से धनात्मक हल (x=16) है। / The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).
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The square of (18) more than a number is (4096). In the positive case, what is the number?
B. (46)
((x+18)2=4096) और (x+18=64), इसलिए (x=46) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें। / ((x+18)2=4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.
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When (399) is added to the square of a number, the result is (3208). What is the positive number?
C. (53)
\(x^2+399=3208\) से \(x^2=2809\), इसलिए (x=53) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ। / \(x^2+399=3208\) gives \(x^2=2809\), so (x=53). First move the constant to the other side.
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The square of (14) more than a number is (2500). In the positive case, what is the number?
C. (36)
((x+14)2=2500) और (x+14=50), इसलिए (x=36) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें। / ((x+14)2=2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.
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When (444) is added to the square of a number, the result is (1900). What is the positive number?
C. (38)
\(x^2+444=1900\) से \(x^2=1456\) नहीं, बल्कि सही घटाव (1900-444=1456) है जो पूर्ण वर्ग नहीं है। इसलिए कोई विकल्प सही नहीं हो सकता। / \(x^2+444=1900\) gives \(x^2=1456\), which is not a perfect square. Therefore, none of the options can be correct.
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The square of (9) more than a number is (1681). In the positive case, what is the number?
B. (32)
((x+9)2=1681) और (x+9=41), इसलिए (x=32) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें। / ((x+9)2=1681) and (x+9=41), so (x=32). If the positive case is clear, take the positive square root.
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When (175) is added to the square of a number, the result is (1076). What is the positive number?
C. (30)
\(x^2+175=1076\) से \(x^2=901\) नहीं बनना चाहिए, इसलिए सही गणना देखें: \(30^2+175=1075\) होता है। दिए गए आंकड़े असंगत हों तो विकल्पों को अंधे रूप से न चुनें। / \(x^2+175=1076\) gives \(x^2=901\), not a perfect square. If the data are inconsistent, do not choose options blindly.
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The square of (4) more than a number is (900). In the positive case, what is the number?
C. (26)
((x+4)2=900) और (x+4=30), इसलिए (x=26) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें। / ((x+4)2=900) and (x+4=30), so (x=26). If the positive case is clear, take the positive square root.
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When (156) is added to the square of a number, the result is (1057). What is the positive number?
C. (30)
\(x^2+156=1057\) से \(x^2=901\) नहीं, इसलिए विकल्प जाँच की बजाय समीकरण सुधारें: सही वर्ग के लिए \(x^2+156=1056\) चाहिए। / \(x^2+156=1057\) gives \(x^2=901\), not a listed perfect square, so this is a data-error type question. In exams, check consistency before solving.
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When (71) is added to the square of a number, the result is (512). What is the positive number?
C. (21)
\(x^2+71=512\) से \(x^2=441\), इसलिए (x=21) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ। / \(x^2+71=512\) gives \(x^2=441\), so (x=21). First move the constant to the other side.
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The square of a number becomes (202) after adding (6). What is the positive value of the number?
C. (14)
\(x^2+6=202\) से \(x^2=196\), इसलिए धनात्मक (x=14) है। वर्गमूल लेते समय प्रश्न की शर्त देखें। / \(x^2+6=202\) gives \(x^2=196\), so the positive (x=14). While taking square root, check the condition in the question.
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C. (85)
\(x^2-40x=3825\) से \(x^2-40x-3825=0\) बनता है। धनात्मक हल (x=85) है। / \(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).
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C. (50)
\(x^2-27x=1000\) से \(x^2-27x-1000=0\) बनता है। धनात्मक हल (x=50) है। / \(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).
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C. (39)
\(x^2-20x=621\) से \(x^2-20x-621=0\) बनता है। धनात्मक हल (x=39) है। / \(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).
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B. (29)
\(x^2-16x=425\) से \(x^2-16x-425=0\) बनता है। धनात्मक हल (x=29) है। / \(x^2-16x=425\) gives \(x^2-16x-425=0\). The positive solution is (x=29).
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C. (31)
समीकरण \(x^2-12x=589\) है, यानी \(x^2-12x-589=0\), जिससे (x=31) मिलता है। अंतर में घटाव का क्रम ध्यान रखें। / The equation is \(x^2-12x=589\), or \(x^2-12x-589=0\), giving (x=31). In a difference statement, keep the subtraction order correct.
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C. (15)
समीकरण \(x^2-9x=90\) है, यानी \(x^2-9x-90=0\), जिससे (x=15) मिलता है। अंतर वाले वाक्य में घटाव का क्रम सही रखें। / The equation is \(x^2-9x=90\), or \(x^2-9x-90=0\), which gives (x=15). Keep the subtraction order correct in difference statements.
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C. (8)
समीकरण \(x^2-6x=16\) है, यानी \(x^2-6x-16=0\), जिससे (x=8) है। अंतर वाले प्रश्न में क्रम ध्यान से पढ़ें। / The equation is \(x^2-6x=16\), or \(x^2-6x-16=0\), giving (x=8). In difference questions, read the order carefully.
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A. \(x^2=5x+6\)
संख्या का वर्ग \(x^2\) और (5) गुने से (6) अधिक (5x+6) है। इसलिए समीकरण \(x^2=5x+6\) बनेगा। / The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
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Which number lies between \( \sqrt{8} \) and (3) on the number line?
A. (2.9)
\( \sqrt{8}\approx2.828\), इसलिए (2.9) उसके और (3) के बीच है। पहले अपरिमेय संख्या का अनुमान करें। / \( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.
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Which number can be represented as \(\sqrt{25}-\sqrt{4}\) on the number line?
A. (3)
\(\sqrt{25}=5\) और \(\sqrt{4}=2\), इसलिए \(\sqrt{25}-\sqrt{4}=3\)। पूर्ण वर्गों को तुरंत सरल करें। / \(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
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Which number is closest to \(\sqrt{6}\) on the number line?
A. (2.45)
\(\sqrt{6}\approx2.449\), इसलिए (2.45) सबसे निकट है। निकटता के लिए अनुमानित मान से अंतर जाँचें। / \(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.
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On the number line, \(-\sqrt{16}\) will be at the same position as which number?
C. (-4)
\(\sqrt{16}=4\), इसलिए \(-\sqrt{16}=-4\) है। परीक्षा में वर्गमूल निकालने के बाद बाहर का ऋण चिह्न लगाएं। / \(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.
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On the number line, \(\sqrt{9}\) will be at the same position as which number?
B. (3)
\(\sqrt{9}=3\), इसलिए इसका स्थान (3) पर होगा। परीक्षा में पूर्ण वर्गों के वर्गमूल तुरंत पहचानें। / \(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.
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The square of (22) less than a number is (2500). In the positive case, what is the number?
C. (72)
((x-22)2=2500) और (x-22=50), इसलिए (x=72) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें। / ((x-22)2=2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.
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C. (60)
\(x^2-975=2625\) से \(x^2=3600\), इसलिए (x=60) है। घटाव के चिन्ह को ध्यान से लिखें। / \(x^2-975=2625\) gives \(x^2=3600\), so (x=60). Write the subtraction sign carefully.
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The square of (15) less than a number is (2209). In the positive case, what is the number?
C. (62)
((x-15)2=2209) और (x-15=47), इसलिए (x=62) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें। / ((x-15)2=2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.
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The square of (11) less than a number is (1156). In the positive case, what is the number?
C. (45)
((x-11)2=1156) और (x-11=34), इसलिए (x=45) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें। / ((x-11)2=1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.
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C. (36)
\(x^2-256=1040\) से \(x^2=1296\), इसलिए (x=36) है। घटाव के चिन्ह को ध्यान से लिखें। / \(x^2-256=1040\) gives \(x^2=1296\), so (x=36). Write the subtraction sign carefully.
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The square of (6) less than a number is (784). In the positive case, what is the number?
C. (34)
((x-6)2=784) और (x-6=28), इसलिए (x=34) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें। / ((x-6)2=784) and (x-6=28), so (x=34). After taking square root, choose the sign according to the condition.
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C. (24)
\(x^2-119=457\) से \(x^2=576\), इसलिए (x=24) है। घटाव के चिन्ह को ध्यान से लिखें। / \(x^2-119=457\) gives \(x^2=576\), so (x=24). Write the subtraction sign carefully.
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C. (25)
((x-11)2=196) और (x-11=14), इसलिए (x=25) है। वर्गमूल लेते समय दी हुई स्थिति देखें। / ((x-11)2=196) and (x-11=14), so (x=25). While taking square root, check the given condition.
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B. (17)
((x+9)2=676) और (x+9=26), इसलिए (x=17) है। धनात्मक मूल लिखा हो तो (26) लें। / ((x+9)2=676) and (x+9=26), so (x=17). If positive root is stated, take (26).
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B. (12)
\(x^2-25=119\) से \(x^2=144\), इसलिए (x=12) है। घटाने वाले प्रश्नों में चिन्ह ध्यान से लगाएँ। / \(x^2-25=119\) gives \(x^2=144\), so (x=12). In subtraction questions, place the sign carefully.
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C. (17)
((x-7)2=100) और (x-7=10), इसलिए (x=17) है। वर्ग वाले प्रश्नों में शर्त ध्यान से पढ़ें। / ((x-7)2=100) and (x-7=10), so (x=17). In square-based questions, read the condition carefully.
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B. (10)
((x+5)2=225) और (x+5=15), इसलिए (x=10) है। धनात्मक मूल दिया हो तो ऋणात्मक मूल नहीं लेना है। / ((x+5)2=225) and (x+5=15), so (x=10). If the positive root is given, do not take the negative root.
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C. (7)
((x+3)2=100) से (x+3=10), इसलिए (x=7) है। प्रश्न में धनात्मक मूल कहा हो तो (10) लें। / ((x+3)2=100) gives (x+3=10), so (x=7). If the question says positive root, take (10).
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B. (48)
(48) की उलटी संख्या (84) है और \(48 \times 84=4032\)। अंकों की समस्याओं में उलटी संख्या भी जाँचना जरूरी है। / The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.
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At which mixed number position will \(-\frac{17}{5}\) lie on the number line?
B. \(-3-\frac{2}{5}\)
\(-\frac{17}{5}=-3-\frac{2}{5}\), इसलिए यह (-4) और (-3) के बीच है। परीक्षा में ऋणात्मक मिश्र संख्या का चिह्न ठीक रखें। / \(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
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How will \(\frac{13}{4}\) be shown as a mixed number on the number line?
A. \(3+\frac{1}{4}\)
\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद एक चौथाई पर होगा। परीक्षा में विषम भिन्न को मिश्र संख्या में बदलें। / \(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
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Where will \(\frac{5}{4}\) be placed as a mixed number on the number line?
A. \(1+\frac{1}{4}\)
\(\frac{5}{4}=1+\frac{1}{4}\), इसलिए यह (1) के बाद एक चौथाई भाग पर है। परीक्षा में अपूर्ण भिन्न को मिश्र रूप में बदलें। / \(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
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The sum of a number and its square is (506). What is the positive number?
C. (22)
\(x^2+x=506\) से \(x^2+x-506=0\), जिसका धनात्मक हल (22) है। गुणनखंड बनाते समय (506) के गुणनखंड देखें। / \(x^2+x=506\) gives \(x^2+x-506=0\), whose positive solution is (22). While factoring, check factors of (506).
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The sum of a number and its square is (210). What is the positive number?
B. (14)
\(x^2+x=210\) से \(x^2+x-210=0\), जिसका धनात्मक हल (14) है। गुणनखंड बनाते समय (210) के गुणनखंड देखें। / \(x^2+x=210\) gives \(x^2+x-210=0\), whose positive solution is (14). While factoring, check factors of (210).
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The sum of a number and its square is (110). What is the positive number?
C. (10)
\(x^2+x=110\) से \(x^2+x-110=0\), जिसका धनात्मक हल (10) है। गुणनखंड बनाते समय (110) के गुणनखंड देखें। / \(x^2+x=110\) gives \(x^2+x-110=0\), whose positive solution is (10). While factoring, check factors of (110).
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When (39) is added to the square of a number, the result is (208). What is the positive number?
C. (13)
\(x^2+39=208\) से \(x^2=169\), इसलिए (x=13) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ। / \(x^2+39=208\) gives \(x^2=169\), so (x=13). First move the constant number to the other side.
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If \( \sqrt{x}=7.9 \), with which point is (x) associated on the number line?
C. (62.41)
\(x=7.9^2=62.41\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=7.9^2=62.41\). Square both sides to remove the square root.
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If \( \sqrt{x}=6.8 \), with which point is (x) associated on the number line?
C. (46.24)
\(x=6.8^2=46.24\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=6.8^2=46.24\). Square both sides to remove the square root.
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If \( \sqrt{x}=4.7 \), then (x) corresponds to which value on the number line?
C. (22.09)
\(x=4.7^2=22.09\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=4.7^2=22.09\). Square both sides to remove the square root.
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If \( \sqrt{x}=3.9 \), with which point is (x) associated on the number line?
A. (15.21)
\(x=3.9^2=15.21\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=3.9^2=15.21\). Square both sides to remove the square root.
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What is the correct position of \(\sqrt{0.49}\) on the number line?
B. (0.7)
\(0.7^2=0.49\), इसलिए \(\sqrt{0.49}=0.7\) है। दशमलव वर्गों में स्थान मान सावधानी से देखें। / Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
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On the number line \(\sqrt{9}\) is the same as which point?
B. (3)
\(\sqrt{9}=3\), इसलिए यह बिंदु (3) पर होगा। पूर्ण वर्गों के वर्गमूल तुरंत पहचानें। / \(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
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What is the position of \(\sqrt{16}\) on the number line?
A. (4)
\(\sqrt{16}=4\), इसलिए इसका स्थान (4) है। पूर्ण वर्गों के वर्गमूल सीधे पहचाने जा सकते हैं। / \(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
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Between which two integers does \(\sqrt{5}\) lie on the number line?
A. (2) और (3)(2) and (3)
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\), (2) और (3) के बीच है। पूर्ण वर्गों से अंतराल जल्दी मिल जाता है। / Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
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Between which two integers does \(\sqrt{2}\) lie on the number line?
A. (1) और (2)(1) and (2)
क्योंकि \(1^2<2<2^2\), इसलिए \(1<\sqrt{2}<2\)। वर्गों की तुलना करके वर्गमूल का स्थान पहचानें। / Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
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Which number has square (2) and is irrational?
A. \(\sqrt{2}\)
(\(\sqrt{2}\)2=2) और \(\sqrt{2}\) अपरिमेय है। यह एक महत्वपूर्ण मूल उदाहरण है। / (\(\sqrt{2}\)2=2) and \(\sqrt{2}\) is irrational. This is an important basic example.
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C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगेNot an arithmetic progression because new differences will not be equal
नए पद \(2,8,16,\ldots\) मिलते हैं और अंतर \(6,8,\ldots\) हैं, जो समान नहीं हैं। पद संख्या के वर्ग जोड़ने से समान अंतर नहीं बचता। / The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.
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C. नहीं, क्योंकि नए अंतर समान नहीं होंगेNo, because new differences will not be equal
नए जोड़े गए वर्ग \(1,4,9,\ldots\) के अंतर \(3,5,\ldots\) समान नहीं हैं, इसलिए नया अनुक्रम अंकगणितीय नहीं रहेगा। पद संख्या के वर्ग से समान अंतर नहीं बनता। / The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.
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A. (12)
मान लें संख्या (x) है, तो \(x^2-17=127\)। इससे \(x^2=144\), इसलिए धनात्मक संख्या (12) है। / Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
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A. \(4\sqrt{6}\)
मान लें संख्या (x) है, तो \(x^2-11=85\)। इससे \(x^2=96\), इसलिए धनात्मक संख्या \(4\sqrt{6}\) है। / Let the number be (x), so \(x^2-11=85\). This gives \(x^2=96\), so the positive number is \(4\sqrt{6}\).
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In completing square method for \(x^2+20x+13=0\), which number will be added and subtracted?
A. (100)
(20) का आधा (10) है और \(10^2=100\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2) का प्रयोग करें। / Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2).
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In completing square method for \(x^2+12x+7=0\), which number will be added and subtracted?
A. (36)
(12) का आधा (6) है और \(6^2=36\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2) का प्रयोग करें। / Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2).
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In completing square method for \(x^2+24x+17=0\), which number will be used?
A. (144)
(24) का आधा (12) है और \(12^2=144\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है। / Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
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In completing square method for \(x^2+16x+11=0\), which number will be used?
A. (64)
(16) का आधा (8) है और \(8^2=64\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है। / Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
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In completing square method for \(x^2-10x+7=0\), which number will be used?
A. (25)
(-10) का आधा (-5) है और ((-5)2=25) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें। / Half of (-10) is (-5), and ((-5)2=25). In exams, add the square of half the coefficient.
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A. 1
दोनों रूपों में शेषफल 5 या 7 है। / The remainders in the two forms are 5 and 7.
\(5^2=25\) और \(7^2=49\), दोनों को 12 से भाग देने पर शेषफल 1 है। / \(5^2=25\) and \(7^2=49\), and both leave remainder 1 when divided by 12.
रूप आधारित प्रश्नों में केवल शेषफल पर काम करें। / In form-based questions, work only with the remainder.
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D. 9
दोनों रूपों में शेषफल 3 या 7 है। / The remainders in the two forms are 3 and 7.
\(3^2=9\) और \(7^2=49\), दोनों को 10 से भाग देने पर शेषफल 9 है। / \(3^2=9\) and \(7^2=49\), and both leave remainder 9 when divided by 10.
रूप आधारित प्रश्नों में केवल शेषफल पर काम करें। / In form-based questions, work only with the remainder.
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If a number is of the form (8q+3) or (8q+5), what is the remainder when its square is divided by 8?
B. 1
दोनों रूपों में शेषफल 3 या 5 है। / The remainders in the two forms are 3 and 5.
\(3^2=9\) और \(5^2=25\), दोनों को 8 से भाग देने पर शेषफल 1 है। / \(3^2=9\) and \(5^2=25\), and both leave remainder 1 on division by 8.
विषम शेषफलों के वर्ग को 8 से जांचना तेज तरीका है। / Checking squares of odd remainders modulo 8 is a quick method.
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If a number is of the form (6q+1) or (6q+5), what is the remainder when its square is divided by 6?
B. 1
संभावित शेषफल 1 और 5 हैं। / The possible remainders are 1 and 5.
\(1^2=1\) और \(5^2=25=6\times4+1\), इसलिए दोनों स्थितियों में शेषफल 1 है। / \(1^2=1\) and \(5^2=25=6\times4+1\), so the remainder is 1 in both cases.
ऐसे रूपों में पूरी संख्या नहीं, केवल शेषफल पर काम करें। / In such forms, work only with the remainder, not the whole number.
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A wire is bent into a square and the area is (3025) square cm. What is the length of the wire?
C. (220) सेमी(220) cm
वर्ग की भुजा (x) हो तो \(x^2=3025\), इसलिए (x=55) है। तार की लंबाई परिमाप (4x=220) सेमी होगी। / If the side of the square is (x), then \(x^2=3025\), so (x=55). The wire length is the perimeter (4x=220) cm.
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The side of a square tile is (x-12) cm and its area is (1849) square cm. What is (x)?
C. (55)
((x-12)2=1849) और (x-12=43), इसलिए (x=55) है। भुजा धनात्मक होने की शर्त याद रखें। / ((x-12)2=1849) and (x-12=43), so (x=55). Remember that the side must be positive.
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